3 essba0o 
3 
Read A & P into store 
Orthogonalise A by making all rows but first 
orthogonal to first row and then:- 
all rows but first two orthogonal to 2nd row 
all rows but first three orthogonal to 5rd row,and so on. 
Make each row of P orthogonal in turn to each row of A 
Read B & Q into store, allowing B to overwrite A 
Orthogonalise B as in (b) 
Make each row of P orthogonal in turn to each row of B 
Make each row of Q orthogonal in turn to each row of P 
(P now no longer needed). 
Make each row of Q orthogonal int urn to each | 
row of B | 
Read C & R into store, allowing C to overwrite B, 
and so on, 
Meanwhile, one will have been accumulating the result vector, x, 
"na. 
in the fashion shown above; it will be seen that by this 
two steps forward, one step back" method, one can invert quite 
a large matrix, without back solution, and while holding only 
parts of 
it in store at a time.